1 (a) (i) State the units for electrostatic force and electric charge.

Transcription

1 1.0: ELECTROSTATIC 1 (a) State the units for electrostatic force and electric charge. A positive test charge, q is placed near a positive fixed charge, Q. As q moves away from Q, describe the motion of the test charge in term of acceleration whether zero, non zero constant, increasing or decreasing. State your reasoning. FIGURE 1 Two equal and opposite charges are a small distance apart, forming an electric dipole. A positive charge +q is placed above these charges, as shown in FIGURE 1, equidistant from both of them. Describe all of the forces and the net force on the charge +q because of the dipole by sketching electric force diagram. FIGURE 2 FIGURE 2 shows two charged particles on an x axis: q = at x = 3.00 m and q = at x = m. Calculate the net electric field produced at pointp at y = 4.00 m? Calculate electric potential at point P due to the two charges. ( Physic s Unit, KML 1

2 2 (a) State the relationship between magnitude of electric force that exists on a point charge due to second point charge with the separation distance between those point charges. FIGURE 1 Two electrons (e 1 and e 2 ) and a proton (p) lie on a straight line, as shown in FIGURE 1. Describe the directions of the force of e 2 on e 1, the force of p on e 1, and the net force on e 1 by sketching electric force diagram. Experiment A uses a test charge q 0 and experiment B uses a test charge 2q 0 to measure an electric field produced by a stationary point chargeq at a location P near the point charge. By using definition of electric field, determine electric field at the location P respectively if you carry out both of the experiments A and B. Compare the result of those experiments A and B. FIGURE 2 Points R and T are each a distance d = 0.10 m from each of two particles with charges of equal magnitudes and opposite signs as shown in FIGURE 2. Magnitude of the charge is 10 μc. Determine the work required to move a particle with negative charge q= 2.0μC from R to T. ( Physic s Unit, KML 2

3 2.0: CAPACITOR AND DIELECTRICS 1 (a) If the electric field between the plates of a given air-filled capacitor is weakened by removing charge from the plates, describe the capacitance of that capacitor whether increase, decreases or does not change. Explain your reasoning. A certain physical quantity is a measure of how quickly a capacitor charges or discharges. State that physical quantity and its unit. FIGURE 1 Describe the connection between 9.0 pf capacitor and 11 pf capacitor. Find the equivalent capacitance between point a and point c. A resistor is connected in series with a capacitor and a battery of 12 V. Before the switched is closed at time t=0 s, the capacitor is uncharged. Sketch and label a circuit to describe the situation. Determine the charge on the capacitor at t=10 s. Physic s Unit, KML 3

4 2 (a) If both the plate area and the plate separation of a parallel-plate capacitor are doubled, Explain and describe the capacitance whether increasing, decreasing or unchanged. A dielectric slab is slowly inserted between the plates of a parallel plate capacitor, while the potential difference between the plates is held constant by a battery. As it is being inserted, describe the capacitance and accumulated charge on each plate whether increasing, decreasing or unchanged. FIGURE 2 FIGURE 2 shows six 6 F capacitors. Determine the capacitance between points a and b. FIGURE 3 Total energy of J is stored in the two identical capacitors shown in FIGURE 3 when they are connected with a power supply of 200V. Determine the capacitance of each capacitor. Physic s Unit, KML 4

5 3.0: ELECTRIC CURRENT & DIRECT CURRENT CIRCUITS 1 (a) FIGURE 1 The figure shows a graph of the resistance of a wire as a function of its length. State the physical quantities does the slope of this graph represent? A 60.0 Ω resistor is connected in parallel with a Ω resistor. This parallel group is connected in series with a 20.0 Ω resistor. The total combination is connected across a 15.0 V battery. Sketch the circuit to describe the situation. Determine the current across the Ω resistor. Determine the power delivered to the Ω resistor. FIGURE 2 Current which is flowing from point f to e through the 14.0 V battery is 3.0 A. Determine the current which is flowing through point a. Physic s Unit, KML 5

6 2 (a) Describe the physical properties in terms of thickness, length and temperature for a copper conductor so that it will have a least resistance. A certain wire has resistance R. Second wire, of the same material, has half the length and half the diameter of the first wire. Determine the resistance of the second wire in term of R. FIGURE 3 In the FIGURE 3, the current in the 3 resistor is 4 A. Determine the potential difference between points 1 and 2. Four 20 resistors are connected in parallel and the combination is connected to a 20 V emf device. Calculate the current in any one of the resistors. FIGURE 4 A potentiometer is balanced when position of the jockey is at point c as shown in FIGURE 4. Determine the length of ac, when galvanometer s reading is zero. Given that and length of wire ab is 1.0 m. Physic s Unit, KML 6

7 4.0 MAGNETIC FIELD 1 (a) Define magnetic field 1 A particle 8.5mC with velocity 4.75kms initially moving northward is deflected toward east in a magnetic field1.25t, State the direction of magnetic field. Illustrate the diagram by drawing the direction of magnetic force and velocity. Calculate the magnetic force on the particle. Calculate the acceleration experienced by the particle given the mass 20 of the particle is kg The springs X and Y, having an original length of 3cm and force constant 3 Nm -1 each, are fixed to two straight insulated wires LM and VW on a smooth horizontal surface as shown in the figure below. When the switch S is turned on, a current of 40 A flows through the wires. Calculate the magnetic force acting on each wire LM and VW The distance between LM and VW when the equilibrium is reached. Physic s Unit, KML 7

8 2. (a) Define 1 ampere. The magnetic field at the centre of a circular coil of radius 5 cm is 60 T. If the number of turn of coil is 4, calculate the current flow through the coil. A heart surgeon monitors the flow of blood through an artery using an electromagnetic flowmeter as shown in the figure below. The blood is known to contain mobile positive ions. Electrodes X and Y make contact with the outer surface of the blood vessel. The separation of the electrodes X and Y is 4 r m. When a magnetic field of flux density 2T is produced by the electromagnet, a potential difference 600V is developed between the electrodes X and Y. When this condition is reached, the blood flows only a certain speed Calculate the magnitude of the electric force on the ion. State the conditions for the blood to flow only at certain speed Calculate the speed for the condition given in. (d) In a moving coil galvanometer,the coil of 400 turns has a rectangular shape of dimensions 3cm x 5 cm. The radial magnetic field has a magnetic flux density of 0.24 T. Calculate the torque on the coil when a current of 0.024A flow in it. Physic s Unit, KML 8

9 5.0: ELECTROMAGNETIC INDUCTION 1 (a) State Faraday and Lenz law A long magnet is removed from the centre of a solenoid as shown in the figure. The coil is connected to a sensitive ammeter. The speed of the magnet is controlled to maintain an induced e.m.f of 60 V across the coil. Removing the magnet in this way takes 2 s. Calculate the change of flux through the coil Calculate current flow in the solenoid if the resistance is 2. Explain the way to verify the polarity of the magnet. A magnetic field B is applied perpendicular to a coil as shown in the figure below. Use Faraday s law to explain briefly how an induced current is produced in the resistor by reducing gradually the magnetic field. Determine direction of the induced current. Explain your answer. Physic s Unit, KML 9

10 2 (a) Define magnetic flux A circular coil with diameter 3 cm is placed in uniform magnetic field 1.5 T. Calculate the magnetic flux through the coil when the plane of the coil makes an angle of 30 to the magnetic field. A rectangular coil ABCD of 60 turns has its plane set parallel to a uniform magnetic field 0.02T as shown in figure.the coil of sides AB and CD are of length 10cm and side BC is of length 8cm. A current I is flowing through the coil. Copy the diagram and draw the direction of the force acting on sides AB and CD respectively. (iv) The current I is then switched off and the coil is rotated about an axis at a constant angular velocity,. Explain why an e.m.f is induced in the coil. Calculate the maximum value of induced emf for the coil given the coil rotates at 120 rev/min. Sketch graphs to show the variation of the magnetic flux linkage through coil with respect to time. A coil P with the length of 50cm and radius 3cm has 1000 turns. The self inductance of the coil is 0.2 mh. If the current flows through it is 4 A, calculate the mutual inductance if a coil Q with 50 turns is placed beside coil P. Physic s Unit, KML 10

11 6.0: ALTERNATING CURRENT 1 (a) The rms output voltage of an AC source is V, and the operating frequency is Hz. Write the equation for the output voltage as a function of time. At what frequency does the inductive reactance of a μh inductor equal to the capacitive reactance of a μf capacitor? A Ω resistor, a 0.10 H inductor and a µf capacitor are connected in series to a Hz AC source. The rms current in the circuit is 2.75 A. Find the rms voltage across the resistor the inductor the capacitor Sketch the phasor diagram for the circuit. To determine the inductance of a coil used in a research project, a student first connects the coil to a V battery and measures a current of 0.63 A. The student then connects the coil to an AC source of V rms = V, f = Hz and measures an rms current of 0.57 A. What is the inductance of the coil? 2 (a) Is the sum of the voltages across the elements in a series RLC circuit greater than or less than the applied voltage? Explain. An AC source with V max = V, f = Hz is connected between points a and d as shown in the figure below. Calculate the maximum voltage between points a and b b and c c and d (iv) b and d An AC voltage in the form of V 100 sin 1000t is applied to a series RLC circuit. If R = Ω, C = 5.00 μf and L = 0.50 H, calculate the average power delivered to the circuit the power factor of the circuit Physic s Unit, KML 11

12 7.0: GEOMETRICAL OPTICS 1 (a) In a Jules Verne s novel, a piece of ice is shaped into a magnifying lens to focus the sunlight to start a fire. Is this possible? A ball is dropped from rest 3.00 m directly above the vertex of a concave mirror that has a radius of 1.00 m and lies in a horizontal plane. At what time do the ball and its image coincide? A concave spherical mirror has a radius of curvature of cm. Find the location of the image for the object distances of cm cm cm For each case, state whether the image is real or virtual and upright or inverted, and find the magnification. At an intersection of hospital hallways, a convex mirror is mounted high on a wall to help avoid collisions. The mirror has a radius of curvature of 0.55 m. Locate and describe the image of a patient m from the mirror. 2 (a) A simple model of the human eye ignores its lens entirely. Most of what the eye does to light happens at the transparent cornea. Assume that this outer surface has a 6.00 mm radius of curvature, and assume that the eyeball contains just one fluid with an index of refraction of Prove that a very distant object will be imaged on the retina, mm behind the cornea. (d) An object positioned cm in front of a lens forms an image on a screen 8.00 cm behind the lens. Find the focal length of the lens. Determine the magnification. Is the lens converging or diverging? Explain. A magnifying glass is a converging lens of focal length cm. At what distance from a postage stamp should you hold this lens to get a magnification of +2.00? For a biconcave lens, the radii of curvature for the two surfaces are cm and cm respectively. The glass has the refractive index of 1.53 for the violet light. For a very distant object, locate and describe the image formed by the violet light. Physic s Unit, KML 12

13 8.0: PHYSICAL OPTICS 1. (a) State Huygens principle. The figure shows a point light source P on the ground. P Draw the wavefront from point P at time t = 1 s and t = 2 s. Clearly show the construction that you make and direction of the ray. A beam of a monochromatic light of wavelength 640 nm passes through a single slit of width 4.8 x 10-3 mm. The screen is located at a distance of 0.5 m away from the slit. Determine the angular width of the central bright fringe the width of the central maxima the number of bright fringe that can be observed. 2. (a) What is meant by coherent sources? Suggest two methods of producing two coherent waves. Two point sources X and Y emits waves of wavelength 2.0 cm in phase. The point P is 5.0 cm from X and 8.0 cm from Y. Another point Q is 10.0 cm from X and 4.0 cm from Y. Determine the path difference of waves X and Y at the point P the path difference of waves X and Y at the point Q the type of interference occurs at point P and Q. In a Young s double slits experiment to determine the wavelength of monochromatic light from a source, the following measurements were made. Separation between two slits = 0.20 mm Distance of screen from the two slits = 55.0 cm Distance between the mth and the (m + 10)th bright fringe = 11.4 mm Determine the wavelength of the monochromatic light. (d) A beam of light composing of two wavelengths, λ 1 and λ 2, is used in a Young s double slits experiment. It is observed that the 4th dark fringe produced by λ 1 coincides with the 3rd bright fringe produced by λ 2 on a screen. If λ 1 has a value of 510 nm, determine the value of λ 2. Physic s Unit, KML 13

14 9.0: QUANTIZATION OF LIGHT 1. (a) What is photoelectric effect? State four most important results from a photoelectric effect experiment. The work function for Cesium is 2.14 ev. (iv) Calculate the maximum wavelength of light that ejects electron from a Cesium target. Determinethe speed of the photoelectrons produced when the Cesium is illuminated by the light of wavelength from question. If light of wavelength 452 nm is illuminated on the Cesium, calculate the maximum kinetic energy of photoelectron. What will happen if a light of wavelength 595 nm is illuminated on the Cesium? Why? 2. (a) What is the energy in electron-volt (ev) of a photon of green light of wavelength 525 nm? For a certain cathode material in a photoelectric effect experiment, a stopping potential of 1.0 V for light of wavelength 750 nm, 2.0V for 500 nm and 3.0 V for 375 nm. Plot a V-f graph based on the date given. Determine the work function for this material. A light of wavelength 200 nm falls on nickel with a work function of 5.1 ev. Determine the kinetic energy, in electron-volt (ev), of the photoelectrons emiited. the stopping voltage. the maximum speed of the photoelectrons. Physic s Unit, KML 14

15 10.0: WAVE PROPERTIES OF PARTICLE 1. (a) State de Broglie s hypothesis and give the relationship between momentum and wavelength of a particle. In an electron diffraction experiment, an electron beam which is accelerated on a potential difference is incident normally on a very thin gold film. If the voltage at the anode is increased, what happens to the circular ring? Give evidence that shows a particle behaves as wave and a wave behaves as particle. An electron has a de Broglie wavelength of m. Calculate the momentum of the electron the kinetic energy of the electron the potential difference required to accelerate the electron. 2. (a) Name two physical differences in the structure of the optical microscope and the electron microscope. Explain the advantage of using an electron microscope. The potential difference between the cathode and anode of a cathode ray tube is 3.0 kv. The separation between the anode and cathode is 50 mm. Determine (iv) the speed of the electrons that emerge from the anode the time taken by the electrons to travel from the cathode to the anode the de Broglie wavelength of the electron beam that emerges from the anode. If the potential difference between the cathode and anode is doubled, describe quantitatively the change to the de Broglie wavelength of the electron beam. Physic s Unit, KML 15

16 11.0: NUCLEUS 1. (a) State three differences between isotopes 16 8O and 17 8 O. An indium (In) nucleus contains 49 protons and 66 neutrons. Write the element in nuclide form. 226 Radon, 88 Ra has atomic mass of u. Calculate the mass defect in atomic mass unit, u, the binding energy in MeV, the binding energy per nucleon. Given :m p = u; m n = u (d) Figure below shows a graph of binding energy per nucleon against nucleon number. From the graph, determine the binding energy per nucleon if a nucleus has nucleon number is 80. Using your answer from d), calculate the binding energy of the nucleus. Physic s Unit, KML 16

17 2. (a) For neutral atoms, how many 238 protons are in the 92 U 202 neutrons are in the 80 Hg The nuclear mass of Copper-63 is u. Determine the mass defect in atomic mass units (u) and kilograms (kg) for copper which has 63 nucleons and a proton number of 29. Calculate the binding energy of the Copper-63 nucleus in MeV. Calculate the binding energy per nucleon of the Copper-63 nucleus. Given :m p = u; m n = u Figure below shows a graph of binding energy per nucleon against mass number. Explain briefly about the stability of following nuclei: Hydrogen-2 ( 2 H) Nickel-62 ( 62 Ni) Uranium-238 ( 238 U) Physic s Unit, KML 17

18 12.0: NUCLEAR REACTION 1. a) Nuclear energy can be produced by the following equation: 2 1 H X 3 2 He 1 0 n Q Identify the element X. State whether the equation is fusion or fission reaction. Justify your answer. Calculate the amount of nuclear energy, Q released. Given: m p = u; m n = u; m H = u; m He = u b) The nuclear equation shown below represents the decay of radium to radon with the release of energy Ra 86Rn 226 Given: 226 Ra = u; 222 Rn = u; 4 He= u 4 2 He (iv) Give a reason why radon (Rn) is more stable than radium (Ra). Calculate the mass defect, in kg, for this reaction. Calculate the energy released in this reaction. Calculate the mass of radium (in kg) required to release 2000 MJ of energy. Physic s Unit, KML 18

19 2. a) State conservation of charge (Z) and nucleon number (A) in a nuclear reaction. b) A reaction of nuclear fission is represented by the following equation U 0n 55Cs 37Rb X 0n energy Use the equation to determine the value of X. (iv) Calculate the mass loss of the above reaction. One atomic bomb uses 100 kg of U-235. Determine the reduction in mass which occurs if all of U-235 undergo fission. How much energy is released in the fission of U-235 in? Given : 235 U= u; 141 Cs= u; 93 Rb; m n = u c) Name two of the form of energies released during nuclear fission. d) State three differences between nuclear fission and nuclear fusion reaction. Physic s Unit, KML 19

20 13.0: RADIOACTIVITY 1 (a) Radioactivity is a random process. Explain what is meant by a random process in this context. A sample of uranium-238 contains atoms. Given that the half-life of uranium-238 is s, find the decay constant, the initial activity of the sample, in Becquerel, the number of uranium-238 atoms remaining after s. Induced radioactive technetium is often used as tracers in medical diagnoses. It has a half-life of 6.0 hours. Determine the mass of technetium which is required to produce a sample of activity 3.7 x 10 6 decays s -1. Given: mass of one mole of technetium is g Besides technetium, give one example of radioisotope used as radioactive tracer in medicine and its application. Physic s Unit, KML 20

21 2. (a) 60 Write decay equations for β emission from a 27 Co nucleus to produce Nickel (Ni). A smoke detector contains a small radioactive source. A typical source contains g of americium-241, which has a half-life of 432 years. Determine the decay constant of americium-241. Calculate the number of nuclei in g of americium-241, given that 241 g contains nuclei. Hence, calculate the activity of g of americium-241. c) Nuclear-powered electronic pacemakers were sometimes used to regulate the heartbeat. Such pacemakers were used inside the body and were powered by a small radioactive source. One type of pacemaker used an isotope of plutonium, Pu-238, as its energy source.pu-238 decays by an alpha emission with a half-life of 88 years. Complete the equation for plutonium decaying into thorium. 238 Pu 92 Th The activity of the source in one such pacemaker, when the pacemaker was fitted, was Bq. The energy released by each alpha decay is 5.5 MeV. Calculate the power of the source 30 years after fitting. Physic s Unit, KML 21